On the other hand if you cook the brown rice long enough, the starch will begin to thicken the soup as well. Not as much as barley does, or as quickly, but it will have an effect. And yes, as was mentioned before, make sure to add a lot of liquid to compensate (about 3 times the amount of rice by volume).
As for cheese to make soup creamy...I just go with cream cheese. But that would negate the health effects of removing cream, methinks!